CSCE 121:509-512
Introduction to Program Design and Concepts, Honors
J. Michael Moore
Spring 2015
Set 14: Plotting Functions and Data
1
Overview of Chapter 15
• Discusses graphing of (mathematical) functions and
data
– Benefits of visualization
– Pitfalls with floating-point approximations
• Introduces programming methodologies that are
useful in doing so
–
–
–
–
typedef
Passing functions as arguments
Default arguments
Standard mathematical functions
• Graphics library as running example
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Set 14: Plotting Functions and Data
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Visualization
• It’s very useful to plot graphs of functions and
data
• You can learn things from a plot that are not
evident in a set of numbers
– Think about a sine curve
• Visualization of data is used in most research
and business areas
• Can communicate large amounts of data
simply
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Set 14: Plotting Functions and Data
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Graphing Simple Functions
• Suppose we want to display on the screen a plot of a
mathematical function, such as f(x) = 1, or f(x) = 2*x,
or f(x) = x*x.
• We’d like to do this in a general way, so that we don’t
have to write new code from scratch every time we
want to plot a different function
• Try to pass in the (mathematical) function as an
argument to a (C++) function!
– Represent the mathematical function as (another) C++
function
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Set 14: Plotting Functions and Data
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Calling a Function that Takes a
Function as an Argument
• Our graphics library has a type of Shape called
Function (name of a class)
• It takes the following arguments:
– A (C++) function that takes one double argument and
returns a double: this calculates the mathematical
function we want to plot on the screen
– Range of values over which the mathematical function is to
be plotted
– Some other bookkeeping stuff for displaying the plot in the
window
• After constructing a specific Function object, it can
be attached to the window and displayed
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Set 14: Plotting Functions and Data
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Specifying an Argument that is a Function
• We need a type for the argument that specifies the
function to be plotted
• Use typedef keyword, which declares a new name for
a type
typedef double Fct(double);
• Now Fct means “a function that takes a double
argument and returns a double”
• Examples of objects of type Fct:
double one(double x) { return 1;} // f(x) = 1
double slope(double x) { return x/2;} // f(x) = x/2
double square(double x) { return x*x;} // f(x) = x*x
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Set 14: Plotting Functions and Data
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Definition of Function Shape
struct Function : Shape {
// constructor
Function(
Fct f,
// f is a (C++) function that has one
// double argument and returns a double
/* more arguments for controlling the display
of the plot of f in the window */
);
/* rest of class description */
};
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Set 14: Plotting Functions and Data
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Using Function Shape
/* ... */
Simple_window win(/* ... */);
Function plot(slope, /* ... */);
// remember slope was already defined
win.attach(plot);
win.wait_for_button();
/* ...*/
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Set 14: Plotting Functions and Data
8
Default Arguments
• The Function Shape constructor has seven
arguments!
– Too many
– Asking for trouble, confusion and error
• Solution: provide default values for some of
the arguments
– Must be “trailing” arguments
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Set 14: Plotting Functions and Data
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Default Arguments Example
struct Function : Shape {
Function(
Fct f,
double r1,
double r2,
Point xy,
int count = 100,
// default value of count is 100
double xscale = 25, // default value of xscale is 25
double yscale = 25); // default value of yscale is 25
};
/* ... */
Function f1(sqrt,0,11,orig,100,25,25);
Function f2(sqrt,0,11,orig,100);
// same as f1
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Set 14: Plotting Functions and Data
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Standard Mathematical Functions
Use #include <cmath> to get access to
abs, ceil, floor, sqrt, cos, sin,
tan, acos, asin, atan, sinh, cosh,
tanh, exp, log, log10, pow, etc.
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Set 14: Plotting Functions and Data
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Warning!
• Floating point numbers are just
approximations of real numbers
– Overflow
– Underflow
– Not precise enough for your needs
– Small inaccuracies (rounding errors) can build up
into huge errors
• Advice:
– Be suspicious about calculations
– Check your results
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Set 14: Plotting Functions and Data
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Acknowledgments
• Photo on slide 1: “Juhan’s 2008 Career
Graph” by Juhan Sonin, licensed under CC BY
2.0
• Slides are based on those for the textbook:
http://www.stroustrup.com/Programming/15_graphing.ppt
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Set 14: Plotting Functions and Data
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